7/8x-2/5x=38

Solution for 7/8x-2/5x=38 equation:

7/8x-2/5x=38

We move all terms to the left:

7/8x-2/5x-(38)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


35x/40x^2+(-16x)/40x^2-38=0

We multiply all the terms by the denominator


35x+(-16x)-38*40x^2=0

Wy multiply elements

-1520x^2+35x+(-16x)=0

We get rid of parentheses

-1520x^2+35x-16x=0

We add all the numbers together, and all the variables

-1520x^2+19x=0

a = -1520; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-1520)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-1520}=\frac{-38}{-3040}
=1/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-1520}=\frac{0}{-3040}
=0
$